CMA Final · Strategic Cost Management · Linear Programming
A feed mix must supply at least 10 units of protein and at least 8 units of fibre. Ingredient X costs ₹6 per kg and gives 2 units of protein and 1 unit of fibre per kg. Ingredient Y costs ₹4 per kg and gives 1 unit of protein and 2 units of fibre per kg. What is the minimum cost of the mix?
The minimum cost is ₹32. The protein and fibre constraints meet at 4 kg of X and 2 kg of Y, costing 24 + 8 = ₹32. The other corner points, 8 kg of X alone (₹48) and 10 kg of Y alone (₹40), cost more.
- A₹40
- B₹48
- C₹32Correct
- D₹36
Explanation
The constraints are 2x + y ≥ 10 and x + 2y ≥ 8. They intersect at x = 4, y = 2. The cost at the feasible corner points is: (8,0) = 48, (0,10) = 40, (4,2) = 24 + 8 = 32. The minimum is ₹32.
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